Rationale

Even after realignment there is considerable variance in fMRI time
series that covary with, and is most probably caused by, subject movements. It
is also the case that this variance is typically large compared to
experimentally induced variance. Anyone interested can include the estimated
movement parameters as covariates in the design matrix, and take a look at an
F-contrast encompassing those columns. It can be quite dramatic. The result is
loss of sensitivity, and if movements are correlated to tas specificity. I.e.
we may mistake movement induced variance for true activations. Because the
movement induced variance is often very large compared to "true"
activations false positives may ensue even from a relatively modest correlation
between task and movement.

Previous work

The problem is well known, and several solutions have been suggested. A
quite pragmatic (and conservative) solution is to include the estimated
movement parameters (and possibly squared) as covariates in the design matrix.
Since we typically have loads of degrees of freedom in fMRI we can usually
afford this. The problem occurs when movements are correlated with the task,
since the strategy above will discard "good" and "bad"
variance alike.

The "covariate" strategy described above was predicated on a
model where variance was assumed to be caused by "spin history"
effects, but will work pretty much equally good/bad regardless of what the true
underlying cause is.

Others have assumed that the residual variance is caused mainly by
errors caused by the interpolation kernel in the resampling step of the
realignment. One has tried to solve this through higher order resampling (huge
Sinc kernels, or k-space resampling).

Assumptions behind Unwarp

The "Unwarp" toolbox is based on a different hypothesis
regarding the residual variance. EPI images are not particularly faithful
reproductions of the object, and in particular there are severe geometric
distortions in regions where there is an air-tissue interface (e.g.
orbitofronal cortex and the anterior medial temporal lobes). In these areas in
particular the observed image is a severely warped version of reality, much
like a funny mirror at a fair ground. When one moves in front of such a mirror
ones image will distort in different ways and ones head may change from very
elongated to seriously flattened. If we were to take digital snapshots of the
reflection at these different positions it is rather obvious that realignment
will not suffice to bring them into a common space.

The situation is similar with EPI images, and an image collected for a
given subject position will not be identical to that collected at another.
Hence, even after a "successful" realignment there will be residual
variance caused by the object having different shape at different time points.
We call this effect susceptibility-by-movement interaction. "Unwarp"
is predicated on the assumption that the susceptibility-by-movement interaction
is responsible for a sizeable part of residual movem nt related variance.

The Realign & Unwarp function

Assume that we know how the deformations change when the subject changes
position (i.e. we know the derivatives of the deformations with respect to
subject position). That means that for a given time series and a given set of
subject movements we should be able to predict the "shape changes" in
the object and the ensuing variance in the time series. It also means that, in
principle, we should be able to formulate the inverse problem, i.e. given the
observed variance (after realignment) and known (esti ated) movements we should
be able to estimate how deformations change with subject movement.

We have made an attempt at formulating such an inverse model, and at
solving for the "derivative fields". A deformation field can be
thought of as little vectors at each position in space showing how that
particular location has been deflected. A "derivative field" is then
the rate of change of those vectors with respect to subject movement. Given
these "derivative fields" we should be able to remove the variance
caused by the susceptibility-by-movement interaction. Since the underlying
model is so re tricted we would also expect experimentally induced variance to
be preserved. Our experiments have also shown this to be true. Indeed one
particular experiment even indicated that in some cases the method will
reintroduce experimental variance that had been obliterated by movement related
variance.

In theory it should be possible to estimate also the "static"
deformation field, yielding an unwarped (to some true geometry) version of the
time series. In practice that doesn't really seem to work, hence the method
deals only with residual movement related variance induced by the
susceptibility-by-movement interaction.

Combined use with FieldMap

This means that the time-series will be undistorted to some
"average distortion" state rather than to the true geometry. If one
wants additionally to address the issue of anatomical fidelity one should
combine Unwarp with a measured field-map. A field-map in the format that Unwarp
expects can be created using the FieldMap toolbox.

The description above can be thought of in terms of a Taylor expansion
of the field as a function of subject movement. Unwarp alone will estimate the
first (and optionally second, see below) order terms of this expansion. It
cannot estimate the zeroth order term (the distortions common to all scans in
the time series) since that doesn't introduce (almost) any variance in the time
series. The measured fieldmap takes the role of the zeroth order term. Refer to
the FieldMap toolbox
and the documents FieldMap.man and FieldMap_principles.man for a description of
how to obtain fieldmaps in the format expected by Unwarp.

What derivatives do we need to model?

If we think of the field as a function of subject movement it should in
principle be a function of six variables since rigid body movement has six
degrees of freedom. However, the physics of the problem tells us that the field
should not depend on translations nor on rotation in a plane perpendicular to
the magnetic flux. Hence it should in principle be sufficient to model the
field as a function of out-of-plane rotations (i.e. pitch and roll). One can
object to this in terms of the effects of shimming (object no longer immersed
in a homogenous field) that introduces a dependence on all movement parameters.
In addition SPM/Unwarp cannot really tell if the transversal slices it is being
passed are really perpendicular to the flux or not. In practice it turns out
thought that it is never (at least we haven't seen any case) necessarry to
include more than Pitch and Roll. This is probably because the individual
movement parameters are typically highly correlated anyway, which in turn is
probably because most heads that we scan are attached to a neck around which
rotations occurr.

On the subject of Taylor expansion we should mention that there is the
option to use a second-order expansion (through the defaults) interface. This
implies estimating also the rate-of-change w.r.t. to some movement parameter of
the rate-of-change of the field w.r.t. some movement parameter (colloquially
known as a second derivative). It can be quite intresting to watch (and it is
amazing that it is possible) but rarely helpful/necessarry.

Re-estimation of movement parameters

In addition to inducing residual (after realignment) movement-related
variance, movement-by-susceptibility distortion changes may bias the estimation
of the movement. For each iteration Unwarp gets a better idea of the true shape
of each scan, and can potentially get a better estimate of movement. In Unwarp
there is an option (default) to re-estimate (do a new realign) the movements
between each iteration of estimating the fields. Our testing indicates that
this is a good idea.

Jacobian intensity modulation

In the defaults there is also an option to include Jacobian intensity
modulation when estimating the fields. "Jacobian intensity
modulation" refers to the dilution/concentration of intensity that ensue
as a consequence of the distortions. Think of a semi-transparent coloured
rubber sheet that you hold against a white background. If you stretch a part of
the sheet (induce distortions) you will see the colour fading in that
particular area (you can also think of future appearance of a tattoo obtained
when young and slim). In theory it is a brilliant idea to include also these
effects when estimating the field (see e.g. Andersson et al, NeuroImage
20:870-888). In practice for this specific problem it is NOT a good idea.

Should I use it?

It should be noted that this is a method intended to correct data
afflicted by a particular problem. If there is little movement in your data to
begin with this method will do you no good. If on the other hand there is
appreciable movement in your data (>1mm or >1deg) it will remove some of
that unwanted variance. If, in addition, movements are task related it will do
so without removing all your "true" activations.

The method attempts to minimise total (across the image volume) variance
in the data set. It should be realised that while (for small movements) a
rather limited portion of the total variance is removed, the
susceptibility-by-movement interaction effects are quite localised to
"problem" areas. Hence, for a subset of voxels in e.g. frontal-medial
and orbitofronal cortices and parts of the temporal lobes the reduction can be
quite dramatic (>90%).

Limitations

It should also be noted that there are several reasons for residual
movement related variance. Notably:

Susceptibility-distortion-by-movement interaction: Is what we deal
with here.

Susceptibility-dropout-by-movement interaction: The susceptibility
induced field inhomogenity will, in addition to distortions, cause signal
loss due to through-plane dephasing (which will not be rephased by
encoding gradients that are all in-plane). This signal modulation will
also change with subject position.

Spin-history effects: The signal will depend on how much of
longitudinal magnetisation has recovered (through T1
relaxation) since it was last excited (short TR→low
signal). Assume we have 42 slices, a TR of 4.2seconds and that
there is a subject z-translation in the direction of increasing slice #
between one excitation and the next. This means that for that one scan
there will be an effective TR of 4.3seconds, which means that
intensity will increase.

Slice-to-vol effects: The rigid-body model that is used by most
motion-correction (e.g. SPM) methods assume that the subject remains
perfectly still for the duration of one scan (a few seconds) and that any
movement will occurr in the few μs/ms while the scanner is preparing
for next volume. Needless to say that is not true, and will lead to
further apparent shape changes.

Unwarp will deal only with the first of these, which means that even after
that correction the other components will remain. It is difficult to say which
of these effetcs dominate. It will depend on ones scanner, and even on the
specific data set.

About method behind Unwarp Toolbox

Acknowledgement

The software was developed in part while JLRA was supported by STINT
(Stiftelsen for internationalisering av högre utbildning och forskning.)

Disclaimer

This software has been tested by the authors on data collected on two
different make MR scanners. Undoubtedly there are numerous bugs that will
surface when more people start using it. We are grateful for bug reports, and
other input, and the more we receive the faster bugs will be weeded out.

Unwarp Toolbox Distribution

Unwarp Toolbox for SPM5 can be downloaded with the latest version of SPM5

If you are on a Macintosh, or some other exotic brand, you will
need to compile spm_dilate_erode.c. It should work to simply cd into your Unwarp_updates
directory, start Matlab and at the Matlab prompt type
>> mex spm_dilate_erode.c

Make sure that /usr/local/'whatever'/Unwarp_updates is
included in your Matlab path ahead of your main SPM distribution.

If (very optional) you want the help in the SPM graphical help (for
the "Realign & Unwarp" button) to reflect Realign and Unwarp
you should rename mod_spm.m spm.m and put it in your main SPM distribution
directory. DONT rename it and leave it in the Unwarp_updates directory!